I suspect not, though it's not an uncommon wish!
There are some finagling things you can do, though. Are your particles inside the nucleus? If so, you could:
1- Identify vesicles with IdentifyPrimary
2- Shrink those objects to their central point, using ExpandOrShrink
3- Identify nuclei with IdentifyPrimary
4- Perform a distance transform on the binary result of step 3 (not sure which module!)
5- MeasureObjectIntensity, measure the intensity of the image resulting from step 4, within each of the points from step 2. The intensity in each dot will be the distance from the edge.
The big caveat is I'm not sure which module to use for step 4, maybe someone can help on that! If your particles are in the cytoplasm, I'm not sure how to flip the distance transform in the other direction, or if we have a function for something like that.